Question

Найдите sin A,если ctg A=2. ​

Answer 1

$ctgA=2\\\\1+ctg^2A=\frac{1}{sin^2A}\; \; \to \; \; sinA=\pm \sqrt{\frac{1}{1+ctg^2A}}=\pm \sqrt{\frac{1}{1+4}}=\pm \sqrt{\frac{1}{5}}=\pm \frac{1}{\sqrt5}=\pm \frac{\sqrt5}{5}$